0
votes
3answers
52 views

Maxwell's Equations Divergence Question

$$ \left\{ \begin{align} \text{div } \textbf{E} & =0, \\ \text{div } \textbf{H} & =0, \\ \text{curl } \textbf{E} & = \frac{-1}{c} \frac{\partial \textbf{H}}{\partial t}, \\ \text{curl } ...
0
votes
1answer
38 views

Maxwell's Equations Curl Question

$$\left\{ \begin{align} \text{div } \textbf{E} &=0, \\ \text{div } \textbf{H} & =0, \\ \text{curl } \textbf{E} & = \dfrac{-1}{c} \dfrac{\partial\textbf{H}}{\partial t}, \\\text{curl } ...
-1
votes
0answers
30 views

Find the center of mass of a region with uniform density [closed]

A region on the graph is bound by the lines $y=x/2$, $y=0$, $x=2$ How can I calculate the center of the mass assuming a uniform density of "p" throughout the region?
1
vote
1answer
37 views

Word Problem, Calculus estimation homework

Roger runs a marathon. His friend Jeff rides behind him on a bicycle and clocks his speed every 15 minutes. Roger starts out strong, but after an hour and a half he is so exhausted that he has to ...
1
vote
1answer
43 views

How to properly generalize a definite integral?

I know, I know. On the can, this problem seems simple. Just take $\int_a^bf(x)\mathrm{d}x$ and write is as $\int f(x)\mathrm{d}x$. However, when I tried to do that on an Engineering Dynamics ...
0
votes
1answer
51 views

Why do these acceleration computations contradict each other?

A rocket follows the path $(y-40)^2=160x$ after traveling vertically to the height of 40 feet (making for a very convenient continuity. The problem asks "If the component velocity in the vertical ...
0
votes
2answers
39 views

Calculate the energy in a circuit containing a resistor

A voltage peak in a circuit is caused by a current through a resistor. The energy E which is dissipated by the resistor is: Calculate E if Can anyone please give me some suggestions where to ...
1
vote
1answer
59 views

Uniform Circular Motion with Banked Road and Car

In Uniform Circular Motion, if a car is rounding a curve at a certain speed, and the angle of the road allows the car to drive around at that speed, that speed is called the "design speed." If the ...
0
votes
2answers
35 views

A object was fired from ground with initial angle $\theta$

so i got that , a object was fired from ground with angule $ \theta $. when the object get the height equal to half of his max height , the velocity of object is $\frac{3}{4}$ of initial ...
1
vote
1answer
75 views

Energy Transfer in a Mechanical System - Standard Pulley Scenario

I understand that this is quite a basic question, I am new to dynamics and have trouble starting off questions, I found it quite difficult to find an example question alike to the one below thus I am ...
1
vote
0answers
39 views

Finding the distance from a parabola (ballistic trajectory) to a point (for use in collision detection)

I need to have some form of collision detection / prevention for an object moving along a ballistic trajectory and a second stationary object on the same plane plane. The ballistic trajectory is ...
1
vote
4answers
105 views

Second order differential equation for acceleration

Can you help me understand and solve this question: A bullet is fired vertically upwards with an initial velocity of $u$. Form a second order differential equation for acceleration and by ...
0
votes
1answer
24 views

Oscillating Object - Homework [closed]

I am forced to post this question here as physics SE refuses homework questions even if tagged with their (severely misleading) 'homework' tag. See my question at: ...
0
votes
1answer
48 views

Deriving Barometric formula

Recall idea gas law: $pV= NkT$ where $p$ equals pressure, V volume, N moles of atoms, k boltzmann's constant, T temperature. Also, density: $\rho = m/V = \mu N/N_A V$ where $\mu$ is average mole mass ...
1
vote
1answer
52 views

Integrating this physics expression

Recall: $dp= \rho g \ dh$ where $dp$ is the change in pressure, $ \rho$ is the constant of density and $dh$ is the change in height. This is a part of fluid dynamics (buoyancy). I am to integrate ...
2
votes
1answer
121 views

Almost done with rolling without slipping problem (physics)

I'm almost done with a problem on rotational mechanics. I've got a golf ball rolling down a hill and I'm to find the value of the angle of the hill so that the ball can roll without slipping if the ...
0
votes
3answers
195 views

Physics problem on angular momentum

Problem. A thin, uniform metal bar, 2.00 m long and weighing 90.0 N, is hanging vertically from the ceiling by a frictionless pivot. Suddenly it is struck 1.50 m below the ceiling by a small 3.00-kg ...
0
votes
3answers
89 views

Coupled mass spring system with damping, I need help with the equation

I know that the equation $mx''+cx'+kx=f(t)$ is used for a normal mass spring system, but I don't know how to express the differential equation for a coupled mass spring system with damping. These are ...
1
vote
2answers
139 views

Free fall with resistance: solution to the ODE

I'm having trouble solving this ODE: $$\ddot x = \mu \dot x^2 - g, \space \space x(0)=x_0$$ This is the ODE that determines the equation of motion of an object with air resistance. $\mu$ is a ...
0
votes
0answers
29 views

Don't understand how this answer is arrived at; dynamic power

According to my notes the fomula for dynmaic energy is $\frac{1}{2}capacitive load \times voltage^2$ and formula for dynamic power is $\frac{1}{2}capaxitive load \times voltage^2 \times switching ...
0
votes
1answer
41 views

Focal point in a parabolic mirror

I'm having trouble with the following problem: "Consider the parabolic mirror given by the equation $z=x^2+y^2$. Show that when the rays of light that travel paralell to the $z$ axis pass through ...
0
votes
1answer
36 views

Need help deriving an expression for average acceleration in terms of displacement and time

I'm having trouble with this math problem. Here's what the questions is asking: Derive an expression for the average acceleration of the cart in terms of displacement and time of travel. Write ...
1
vote
1answer
76 views

Does distance increase equally in equal time intervals under the influence of gravity?

Quick question. If an object falls under the influence of gravity near the Earths surface, is the distance traveled increased by equal amounts in equal time intervals? I thought that this would be ...
0
votes
1answer
84 views

Solving an ODE with Mathematica, using Lagrangian mechanics

Question: The velocity of light above a hot surface decreases with the height from that surface. The velocity is given by $v=v_0(\frac{1-y}{\alpha})$ where $y$ is the vertical distance above the ...
4
votes
0answers
228 views

Modelling a Water Rocket. Requires Some Validation and Help. ( WARNING : Extremely Long but Interesting Post )

Good day people of math.stackexchange.com This is a pet project that I plan to use to convince my Prof that I would rather try something similar to this than to do the prescribed project. Edit : ...
0
votes
1answer
44 views

Initial conditions of a second-order ODE

This may look like a physics problem, but everything physical is explained below and I am looking for a mathematical solution. An RLC circuit (pictured above) is governed by two equations: $$ ...
0
votes
2answers
45 views

Re-arranging variables

In physics, you can say that: $T-m_2 g = m_2 a$ And that $ m_1 g - T = m_1 a$ So this, when combined, should equal: $a = \frac{m_1}{m_1 + m_2} \cdot g$ How do they arrive at that conclusion? I ...
1
vote
2answers
31 views

Finding the magnitude of a vector product between two vectors?

Vector $\overrightarrow{A}$ has magnitude $11.0m$ and vector $\overrightarrow{B}$ has magnitude $16.0m$ . The scalar product $\overrightarrow{A}\bullet \overrightarrow{B}$ is $79.0m^2$. What is the ...
0
votes
3answers
63 views

Boxes on a slope [closed]

A box with friction slides down a slope and takes 2 times longer than a similar box with no friction takes to slide the same slope. What is $ \mu $ (the coefficient of friction)? I'm pretty lost. I ...
0
votes
1answer
27 views

Trying to understand free body diagram [closed]

Please consider the following image: Now I'm just trying to understand how exactly this thing is rotated...I'm looking at it exactly like on the image of the car...So the normal force is slightly ...
-1
votes
2answers
54 views

Modeling with First Order Equations [closed]

A ball with mass 015kg is thrown upward with initial velocity 20m/s from the roof of a building 30m high. There is air resistance of magnitude v^2/1325 directed opposite to the velocity , where the ...
1
vote
1answer
55 views

Forces and line of action

A force $F_1 = i - 3j -2k$ at the point $r_1 = -2i + 9j$ another force $F_2 = 2i + j -3k$ at the point $r_2 = i + yj -k$ and a third force $F_3$ are equivalent to zero. Find y for this to be possible. ...
0
votes
1answer
63 views

Problem with friction [closed]

Imagine two boxes stacked on top of each other. The bottom box is larger than the top box and it rests on a surface. So: Between the boxes is a friction force constant $\mu_s$ and between the ...
0
votes
1answer
38 views

What is the most tension I could get [closed]

Look at the following picture: Imagine that mass "m" is very large. What is the maximum tension we can get on the rope? I'm not sure how to understand this. The rope is indestructible I guess, so ...
1
vote
0answers
42 views

Derivatives of polar coordinates

I've got a problem for which I'm trying to calculate $\ddot r$. The problem is right here for the sake of reference. So far, I've got that: $$\ddot r=\frac{d}{dt}v_r=\frac{dv_r}{dr}\frac{dr}{dt}$$ ...
1
vote
1answer
52 views

Vector functions applied to a football game

A wide receiver is standing $40$ ft to the left ($x=-40ft$) of the quarterback who is standing at the origin. The receiver immediately accelerates at $\displaystyle 9.79 \frac{ft}{s^2}$ at an unknown ...
0
votes
0answers
154 views

Calculate uncertainty of the gradient

In my case I have a directly proportional relation between the dependent and independent variables, i.e. $y=mx$. I know the uncertainty of $y_i$ is $\Delta y_i$ and uncertainty of $x$ is $\Delta x$. ...
1
vote
0answers
65 views

Continuity in a physical context

I'm currently trying to solve an exercise for my quantum mechanics class and have run into a bit of a jam: Suppose we have the following potential : $V(x) = 0$ if $x > |a/2|$ but $V(x) = V_0$ if ...
2
votes
0answers
30 views

How to calculate the following 3D ${\bf k}$-space integral?

I'm struggling to calculate$$ \sum_{a,b=\pm}\int\frac{\text d\mathbf{k}}{(2\pi)^3} ...
0
votes
1answer
47 views

Vector functions and motion along a curve

A particle moves along the curve $x=\ln y$ with a constant speed of $4$ units per second. Find the normal scalar component of acceleration as a function of $x$. Honestly, what I don't understand ...
2
votes
1answer
491 views

Solving differential equation regarding temperature change (Newton's law)

I'm solving a differential equation problem set and I bumped into the following DE problem where I got few question marks: The temperature of a body at time $t$ is $T(t)$ and the temperature of ...
2
votes
1answer
57 views

Mechanics - Homework

A stone is thrown vertically down from a high building with an initial velocity of $4\;\mathrm ms^{-1}$. Calculate the time required for the stone to travel $30\;\mathrm m$. So far I have tried using ...
0
votes
1answer
61 views

Work done by gravitational force

In my calculus class we learned about line integrals, and for homework we have exercise to find work done by gravitational force on material dot with mass $m$ which follows path of the elipse ...
1
vote
1answer
131 views

Calculus Related Rates Question [duplicate]

A baseball diamond is a square with side length $90$ ft. A batter hits the ball and runs toward first base with a speed of $f(t)$ ft/s after $t$ seconds. At what rate is the batter's distance to ...
2
votes
3answers
101 views

Velocity of a Particle

Consider a particle moving in a straight line from the fixed point $(0,2)$ to another $(\pi,0)$. The only force acting on the particle is gravity. How would we parametrically define the motion of ...
1
vote
0answers
95 views

Having trouble deriving 2d heat conduction problem

Basically, one of the problems stated to use the second law of thermodynamics to derive the laplace equation: $$\nabla^2_{r,\theta} = \frac{\delta^2}{\delta r^2} + \frac{1}{r}\frac{\delta}{\delta r} ...
-1
votes
1answer
38 views

How do I make these two numbers into a ratio of each other?

The numbers are forces and he wants us to put them in a ratio in order to compare them, but I'm really bad at ratios so. $ 2.69 \cdot 10^{-8} $ Newtons is obviously smaller than $ 2.23 \cdot 10^{-7} ...
0
votes
2answers
150 views

How to calculate centre of mass of an object

I'm new here and this is my first post so please forgive me if I've not posted it in the right place! It's an Engineering related question but as maths is involved I thought it may be appropriate to ...
0
votes
2answers
6k views

Find coefficient of static friction if given initial velocity and distance?

I'm trying to work a physics problem about how to find the coefficient of static friction between two objects when given the initial velocity and distance. Specifically, the problem I am working is as ...
6
votes
1answer
74 views

Solution form for Stokes flows

If $p:\mathbb{R^3} \rightarrow \mathbb{R} $ and $u: \mathbb{R}^3 \rightarrow \mathbb{R}^3$ satisfy: $$\nabla p-\nabla^2u=0$$ $$\nabla\cdot u=0$$ How can we prove that every solution is of the form: ...